A lot depends on the game I am playing.

In RP mode I just go with the plot, so here there is no strategy or reasoning to be applied if not for yours or your race point of view on the matter.

If I am playing Human vs Human, knowing that my adversary is smarter than the AI, I use them lots and put that into consideration regardless the RP purpose. Obviously some races still may not use them to favor another detection strategy such as Patrol Vessels or big silent AWACS, but detection is usually a focal point in these games especially if you have multiple races staring in the same system. Protection will be another important point in this case, so specialized garrisons and STOs are often used in these sites.

If I am just "playing" then I use DTS only on the key worlds to provide extra detection capability to my defense network.

I use them for all strategic systems. They are expensive, but they are a "drop and forget" emplacement vs. putting down stations/buoys/ships. Once built, they are maintenance free and they stack, so you can move them around as needed or redeploy them quickly with freighters. IMO, especially early, they are invaluable to spotting and providing intel on NPRs.

They definitely belong on any colony that you have a stake on, otherwise you wouldn't even know if something hostile is in orbit. As for DSTS-only listening posts, the question is how much minerals and industry you need to invest to cover something that matters, a question heavily dependent on system geography. Form an RP perspective I don't put garrisons on as they're supposed to be secret (usually), stationing tens of thousands of soldiers exponentially increases the chance that the location would become known. gameplay-wise, ground forces also have a signature that can be detected. But if your secrecy fails and a competitor discovers it they can swoop in and take over some potentially expensive hardware, so it's a risk.

If that's for role-play, then I consider adding a company or a battalion, so a 100 to 500 men garrison equipped with 2nd rate weapons. I'm pretending this is a discreet installation, but they deserve to have a token security, it makes sense to me, realism wise.
Granted, they achieve nothing defense-wise ... Unless, unless ... it means a NPR has to divert some assets to overwhelm them with some ground forces. And this case, they bought some time.

They definitely belong on any colony that you have a stake on, otherwise you wouldn't even know if something hostile is in orbit. As for DSTS-only listening posts, the question is how much minerals and industry you need to invest to cover something that matters, a question heavily dependent on system geography. Form an RP perspective I don't put garrisons on as they're supposed to be secret (usually), stationing tens of thousands of soldiers exponentially increases the chance that the location would become known. gameplay-wise, ground forces also have a signature that can be detected. But if your secrecy fails and a competitor discovers it they can swoop in and take over some potentially expensive hardware, so it's a risk.

I put around 20 on every system's capital colony.

I have pushed the scanning range for signature-1000 ships to Ceres, from Earth. It seems a nice addition to my surveillance toolset. What about you, how often do you drop DSTS? Only for populated colonies, or on the contrary to you disperse them on asteroids in many systems, as forward warning outposts with low signature?

Do you add a small garrison for roleplay?